As far as I understand it there are two things in play:
shops ALL AROUND EU selling electronics imported from China without the "European" CE..how is it possible then to be illegal to sell those stuff in Europe but still everyone does?
Enforcement of this is very weak. Pretty much nothing will happen unless somebody complains.
But the big loophole seems to be whether something is a "component" or a "product". If it's something like an ESP that's intended to be incorporated into a larger circuit or another product, then it counts as a "component". If it's sold to consumers as a finished product, with a case and everything, then it's a product.
The CE Marking Association has a good description. Note their enforcement examples. They're concerned with actual risk. Effectively, if your product is found to be unsafe or emitting unacceptable RF, and this causes a problem, then the CE process is a way of punishing that.
I have read that I can put the CE by myself but if asked by authorities I need to prove it.
Yes. It's self-certification, but you're supposed to keep a "technical file" detailing how you checked conformance, and which ETSI standards you checked against.
Are there fines if they find something?
Up to £5k or three months in jail, but according to that webpage the jail sentence has never been given out.